The species was initially described from a partial skeleton found by grazier Doug Langdon in 1963 at Rosebery Downs Station beside Thomson River near Muttaburra, Queensland, Australia, which also provides the creature's generic name. The remains were collected by paleontologist Dr Alan Bartholomai and entomologist Edward Dahms. After a lengthy preparation of the fossils, it was named in 1981 by Bartholomai and Ralph Molnar, who honoured its discoverer with its specific namelangdoni.[3]

The holotype, specimen QM F6140, was found in the Mackunda Formation dating to the Albian-Cenomanian. It consists of a partial skeleton with skull and lower jaws. The underside of the skull and the back of the mandibula, numerous vertebrae, parts of the pelvis, and parts of the front and hind limbs have been preserved.

Some teeth have been discovered further north, near Hughenden,[4] and south at Lightning Ridge,[4] in northwestern New South Wales. At Lightning Ridge there have been found opalised teeth and a scapula that may be from a Muttaburrasaurus. A skull, known as the "Dunluce Skull", specimen QM F14921, was discovered by John Stewart-Moore and 14-year-old Robert Walker on Dunluce Station, between Hughenden and Richmond in 1987. It originates from somewhat older layers of the AllaruMudstone and was considered by Molnar to be a separate, yet unnamed species, a Muttaburrasaurus sp.[4] The same area produced two fragmentary skeletons in 1989. There have also been isolated teeth and bones found at Iona Station southeast of Hughenden.

Muttaburrasaurus was about 8 metres (26 ft) and weighed around 2.8 metric tons (3.1 short tons).[5] The femur of the holotype has a length of 1015 millimetres.

Whether Muttaburrasaurus is capable of quadrupedal movement has been debated; it was originally thought to be an "Iguanodontid"; thought recent studies indicate a rhabdodont position. Ornithopods this basal were incapable of quadrupedal movement. Originally reconstructing Muttaburrasaurus with a thumb spike, Molnar later doubted such a structure was present.[4] The foot was long and broad, with four toes.

The skull of Muttaburrasaurus was rather flat, with a triangular cross-section seen from above, the back of the head being broad but the snout pointed. The snout had the form of a strongly enlarged, hollow, upward-bulging nasal muzzle that might have been used to produce distinctive calls or for display purposes. However, as no fossilised nasal tissue has been found, this remains conjectural. This so-called bulla nasalis was shorter with the older Muttaburrasaurus sp., as is shown by the Dunluce Skull. The top section of the bulla of the holotype has not been preserved, but at least the second skull has a rounded profile.[4]

Muttaburrasaurus had very powerful jaws equipped with shearing teeth. Whereas in more derived euornithopod species the replacement teeth alternated with the previous tooth generation to form a tooth battery, with Muttaburrasaurus they grew directly under them and only a single erupted generation was present. This precluded a chewing motion. An additional basal trait was the lack of a primary ridge on the teeth sides, showing eleven lower ridges. In 1981 Molnar speculated that these qualities indicated an omnivorous diet, Muttaburrasaurus at times eating carcasses. In 1995 he changed his opinion, presenting them as a convergence to the ceratopsian shearing teeth system. They would have been an adaptation for eating tough vegetation such as cycads.[6]